Density
Mass and volume
People often think that materials such as rocks or metals are heavier than objects such as feathers or polystyrene. This is not always true. A very large block of polystyrene may have a larger mass than a small piece of metal.
Think about the food containers and the nails in the pictures.
The food containers are made from polystyrene. They feel very light, because they have a large volume and a small mass. The containers are also hollow, which means they have a space filled with air inside them.
The nails are made from iron. The nails feel heavy because they have a high mass and a small volume. The nails are also solid. The word solid in this case means that each nail has no space with air inside. The word solid can be used as the opposite of hollow.
One of the polystyrene food containers has a larger mass than one of the nails. However, the same volume of iron has a larger mass than the same volume of polystyrene.
We use the word density to describe this difference.
Calculating volume
When calculating the volume of a regular block of material, we measure the lengths of the sides. When talking about a block of material, regular means that we can use an equation to calculate its volume.
This block of wood has a regular shape. The lengths of its sides have been measured.
You can work out the volume of the block by multiplying the lengths of the sides:
10 × 6 × 4 = 240 mm³
The unit is mm³ because the lengths of the sides are in millimetres.
It does not matter in what order you multiply the sides.
Try multiplying the numbers in a different order. You will get the same answer.
If the shape of the material is irregular, then we work out the volume using the displacement method. Irregular means the sides or angles of the shape are not equal. The object is placed into a measuring cylinder of water. The increase in volume of the water is the volume of the object.
This piece of rock has an irregular shape.
It is placed into a measuring cylinder containing 40 cm³ water:
The water rises to the 56 cm³ mark. So, the volume of the rock is:
56 − 40 = 16 cm³
The unit is cm³ because the measuring cylinder measures in cm³.
Calculating density
We say that iron has a higher density than polystyrene. Density means mass per unit volume.
A solid block of iron measuring 1 cm × 1 cm × 1 cm has a mass of 7.9 g.
A solid block of polystyrene measuring 1 cm × 1 cm × 1 cm has a mass of 0.05 g.
We can calculate density using the equation:
density = mass / volume
or using the formula triangle shown here.
Because density is mass divided by volume, the unit of density is the unit of mass divided by the unit of volume. For example:
- if mass is in g and volume is in cm³ then density will be in g/cm³
- if mass is in kg and volume is in m³ then density will be in kg/m³
This leads to the definition of density: density is mass per unit volume of a substance.
Using the example of the block of iron
volume = 1 cm × 1 cm × 1 cm = 1 cm³
mass = 7.9 g
density = 7.9 / 1
= 7.9 g/cm³
We say that iron has a density of 7.9 g/cm³.
Using the example of the polystyrene
volume = 1 cm × 1 cm × 1 cm = 1 cm³
mass = 0.05 g
density = 0.05 / 1
= 0.05 g/cm³
We say that polystyrene has a density of 0.05 g/cm³.
Comparing densities
This table shows the densities of some materials:
| material | helium | air | wood | water | concrete | aluminium | osmium |
|---|---|---|---|---|---|---|---|
| density in g/cm³ | 0.00018 | 0.0012 | 0.35 – 0.95 | 1.0 | 2.4 | 2.7 | 22 |
Look at the densities of the materials in the table. Helium and air are gases. Gases have lower densities than liquids or solids because the particles in a gas are far apart.
As particles in a material get packed closer together, the density of the material increases. So, the materials with the highest densities are all solids.
For the elements, the density usually increases as the atomic number increases. Osmium has atomic number 76 and is more dense than iron, which has atomic number 26.
Did you know, the substance with the highest density in the universe is found in collapsed stars? The forces in collapsed stars are so large that atoms are compressed into very small spaces. This material is called neutronium and has a density of 100 000 000 000 000 000 g/cm³.
One teaspoon of neutronium would have a mass of 500 million tonnes.
Floating and sinking
Look at the densities of some of the materials in the table. Compare their densities with the density of water. What do you notice about the densities of materials, such as wood, that float on water?
You can tell whether something will float or sink in water by comparing its density with that of water.
- If something is more dense than water, it will sink in water.
- If something is less dense than water, it will float in water.
Some objects, such as floats that are used in swimming pools, are designed to have a very low density. These objects are made from materials such as polystyrene, or they are hollow with only air inside.
Modern ships are built from steel that has a density of 8–9 g/cm³.
That is much more than the density of water, which is 1.0 g/cm³.
Some of the largest ships have a mass of over 500 000 000 kg.
So, how do they float in water?
Ships are not solid blocks of steel. There are large spaces inside ships that contain only air. That means the ship has a very large volume, so the average density of the whole ship is less than the density of water. The average density is the mass of all the materials in the ship, including the air, divided by the total volume of the ship.
The density of a ship changes when its mass changes. Cargo, passengers and fuel all add mass to a ship, which increases its density. The density of the ship in the picture is too high, because of the mass of the cargo.
Liquids of different density
When liquids are added together carefully, the less dense liquids will float on the more dense liquids. The liquids that do not mix will form separate layers.
The picture shows what happens when some different liquids are added together.
layered by density
Crude oil is less dense than water. So, when crude oil spills out of ships or out from oil wells, the oil floats on the water. The photograph shows black oil being washed up on a beach. Oil spilling from ships is a major source of water pollution.
Gases and liquids
Gases are less dense than liquids because the particles in a gas are much further apart than in a liquid.
Drops of rain fall down because the water in the drops is more dense than air.
The gas in fizzy drinks is carbon dioxide. Carbon dioxide has a density of 0.002 g/cm³. The liquid in most drinks has a density close to 1.0 g/cm³, as the drinks are mostly water. This difference in density explains why the bubbles of gas in a fizzy drink rise to the top. The gas is a lot less dense than the liquid.
Gases of different density
Gases have lower densities than solids or liquids, but not all gases have the same density. Helium is one of the least dense gases. Helium is sometimes used to fill balloons. A balloon filled with helium will float in air because the balloon and gas is less dense than the air. The balloons in the picture have floated up through the air.
Hydrogen gas is even less dense than helium, but is not used to fill balloons because hydrogen forms an explosive mixture with air.
Solids and liquids are very difficult to compress because their particles are already in contact. Gases are easy to compress because their particles are far apart. When a gas is compressed, the same number of particles is in a smaller volume, so the density of the gas increases. Also, if a gas expands, the same number of particles is in a larger volume, so the density of the gas decreases.
Heat causes a gas to expand. That explains why a hot air balloon can float because the hot air inside the balloon is less dense than the colder air outside.
Questions
- pine wood 0.41 g/cm3
- polycarbonate 1.2 g/cm3
- polyethene 0.95 g/cm3
- water 1.0 g/cm3
b i Which of these materials will sink in water?
b ii Explain why the material will sink in water.
Show Answer
a. Pine wood (0.41 g/cm³) has the lowest density.
b i. Polycarbonate (1.2 g/cm³) will sink.
b ii. It sinks because its density is greater than that of water (1.0 g/cm³).
density = ___________
b A block of aluminium has a volume of 5.0 cm3 and a mass of 13.5 g. Calculate its density (g/cm3).
c Explain whether the block will float or sink in water.
Show Answer
a. density = mass / volume
b. 13.5 g ÷ 5.0 cm³ = 2.7 g/cm³
c. Since 2.7 g/cm³ > 1.0 g/cm³ (water), the aluminium block will sink.
3. The diagram shows a block of wood.
b The block has a mass of 54 g. Calculate its density (g/cm³).
c Explain whether it will float or sink in water.
Show Answer
a. Volume = 6 cm × 4 cm × 3 cm = 72 cm³
b. Density = 54 g ÷ 72 cm³ ≈ 0.75 g/cm³
c. 0.75 g/cm³ < 1.0 g/cm³, so it will float.
a Calculate its density (kg/m³).
b Pure water has a density of 1000 kg/m³. Explain what happens to a block with density 1020 kg/m³ when placed in:
i sea water ii pure water
Show Answer
a. Density = 10 300 kg ÷ 10 m³ = 1030 kg/m³
b i. In sea water (1030 kg/m³) the 1020 kg/m³ block is less dense → it floats.
b ii. In pure water (1000 kg/m³) the block is more dense → it sinks.
a Find the mass of copper with volume 20 cm³.
b Find the volume of copper with mass 4.5 g.
Show Answer
a. Mass = 8.96 g/cm³ × 20 cm³ = 179.2 g
b. Volume = 4.5 g ÷ 8.96 g/cm³ ≈ 0.50 cm³
6. A toy car is placed in water as shown:
b The car has a mass of 84 g. Calculate its density (g/cm³).
c The car is steel + plastic (steel 7.8 g/cm³). Suggest two reasons why the density in b is different.
Show Answer
The water rises from 50 cm³ to 80 cm³.
a. Volume displaced = 30 cm³.
b. Density = 84 g ÷ 30 cm³ ≈ 2.8 g/cm³.
c. (1) Parts of the car are plastic, which is less dense than steel. (2) Air spaces inside the car reduce the overall density (or measurement uncertainty in volume/mass).
| Liquid | Density (g/cm³) |
|---|---|
| kerosene | 0.81 |
| mercury | 14.00 |
| water | 1.00 |
Show Answer
Layer A (top): Kerosene | Layer B (middle): Water | Layer C (bottom): Mercury
8. Zara wants a party balloon that will float in air.
State the property of the gas in the balloon needed to make the balloon float.
Show Answer
The gas must be less dense than air (e.g., helium or hot air) so the balloon’s overall density is lower than the surrounding air.
Show Answer
In the cool mornings and evenings the outside air is denser, so the temperature (and density) difference between the hot air inside the balloon and the ambient air is larger, giving more lift. Mid-day air is warmer and less dense, so the balloon gains less buoyancy.
Think Like a Scientist
Densities of irregular objects
In this investigation, you will calculate the densities of irregular objects.
a balance, measuring cylinders of various sizes, water, a calculator, small irregular objects that will sink in water and will fit inside the measuring cylinders.
Do not drop heavy objects into glass measuring cylinders; either use a plastic measuring cylinder, or hold the glass measuring cylinder at an angle, so that the object slides down slowly.
- Measure the mass of each object in grams. Remember to check that the balance is reading 0.0 g before you place the object on the balance.
- Use the displacement method to calculate the volumes of your objects in cm³.
- Calculate the density of each object using the volumes and masses that you measured.
- Record your results in a table.
Show Answer
To avoid parallax error and take an accurate reading from the bottom of the meniscus.
Show Answer
You would gently push the object fully under the water using a thin, non-absorbent rod or mesh, then measure the volume of water displaced. The displacement must only be measured once the object is completely submerged.
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Use a larger overflow can or displacement container. Fill it with water until it starts to overflow, then carefully place the object inside. Collect and measure the volume of displaced water using a measuring cylinder.
Show Answer
Wood normally has a density much lower than 5.27 g/cm³. That value is closer to metals like iron. The result is likely incorrect and may be due to a mistake in mass or volume measurement, so Sofia is correct.